A circle with area $36\pi$ has a sector with a $45^\circ$ central angle. What is the area of the sector? ${36\pi}$ $\color{#9D38BD}{45^\circ}$ ${\dfrac{9}{2}\pi}$
Solution: The ratio between the sector's central angle $\theta$ and $360^\circ$ is equal to the ratio between the sector's area, $A_s$ , and the whole circle's area, $A_c$ $\dfrac{\theta}{360^\circ} = \dfrac{A_s}{A_c}$ $\dfrac{45^\circ}{360^\circ} = \dfrac{A_s}{36\pi}$ $\dfrac{1}{8} = \dfrac{A_s}{36\pi}$ $\dfrac{1}{8} \times 36\pi = A_s$ $\dfrac{9}{2}\pi = A_s$